conundrum

1. a riddle, the answer to which involves a pun or play on words, as What is black and white and read all over? A newspaper.
2. A paradoxical, insoluble, or difficult problem; a dilemma.
3. A kind of riddle based upon some fanciful or fantastic resemblance between things quite unlike; a puzzling question, of which the answer is or involves a pun.
4. A question to which only a conjectural answer can be made.

Source: dictionary.reference.com
http://dictionary.reference.com/browse/conundrum